If each element of the weighting vector \(\mathbf {f}\)  is drawn uniformly randomly from a set containing all possible weighing coefficients, low mutual correlation of \(\mathbf {F}_\mathrm {h}\)  can be achieved and thus \(\mathbf {m}\)  can be accurately recovered from about \(s \log N\)  random incoherent measurements with high probability [1]}, where \(s\)  is the number of faulty reflecting elements (i.e., the sparsity of \(\mathbf {x}\) ).
Therefore, the diagnostic time can be significantly shortened by exploiting the failure sparsity.
